Convergence results for stochastic convex feasibility problem using random Mann and simultaneous projection iterative algorithms in Hilbert space

Abstract

Real life problems are entrenched in ambiguities. To deal with these ambiguities, stochastic functional analysis has emerged as one of the mathematical tools for solving these kinds of problems. The purpose of this paper is to extend the convergence results of deterministic convex feasibility problems to a stochastic convex feasibility problem and prove that the solution of a convex feasibility problem generated by random Mann-type and Simultaneous projection iterative algorithms with firmly non-expansive mapping converge in quadratic mean and consequently in probability to random fixed point in Hilbert space. These results extend, unify, and generalize different established deterministic results in the literature.

Keywords:

• Convex feasibility problem
• random fixed point
• random operator
• non-expansive mapping
• convergence and Hilbert space

MATHEMATICS SUBJECT CLASSIFICATION:

• 47H07
• 49M05
• 54H25
• 58J65

Acknowledgments

The authors wish to thank the anonymous referees for their comments.